Upper and lower bounds for the pull-in voltage and the pull-in distance for a generalized MEMS problem

Abstract

<abstract><p>We study upper and lower bounds for the pull-in voltage and the pull-in distance for the one-dimensional prescribed mean curvature problem arising in MEMS</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left \{\begin{array}{l} - \left( \frac{u^{ \prime } (x)}{\sqrt{1 +\left (u^{ \prime } (x)\right )^{2}}} \right)^{ \prime } = \frac{\lambda }{(1 -u)^{p}} , \ \ u &lt;1 , \ \ -L &lt;x &lt;L, \\ u ( -L) = u (L) = 0, \end{array}\right . \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ \lambda &gt; 0 $ is a bifurcation parameter, and $ p, L &gt; 0 $ are two evolution parameters. We further study monotonicity properties and asymptotic behaviors for the pull-in voltage and pull-in distance with respect to positive parameters $ p $ and $ L $.</p></abstract>